Learning Set Functions with Implicit Differentiation

Ou et al. [1] introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model. This approximation yields iterations of fixed-point update steps during mean-field variational inference. However, as the number of iterations increases, automatic differentiation quickly becomes computationally prohibitive due to the size of the Jacobians that are stacked during backpropagation. We address this challenge with implicit differentiation and examine the convergence conditions for the fixed-point iterations. We empirically demonstrate the efficiency of our method on synthetic and real-world subset selection applications including product recommendation and set anomaly detection tasks.